Electromechanical resonator

ABSTRACT

An electromechanical resonator is provided incorporating a vibrating reed driven by electrostatic forces between itself and an output electrode. The output is represented by capacitance changes between the reed and an output electrode. Multiple resonators may be used to form band-pass filters and the like.

United States Patent Zakaria ELECTRQMECHANICAL RESONATOR [72] Inventor:Hisham Mohamed Saadallah Zakaria, London, England 73 Assignee:International Standard Electric Corporation, New York, NY.

221' Filed: Feb.l1, 1970 21 Appl.No.: 10,409

[30] Foreign Application Priority Data March 7, 1969 Great Britain..12,218/69 [52] US. Cl. ..333/71, 333/72, 310/82, 317/249, 200/181,310/6 Traub ..333/76 1451 Aug. 22, 1972 3,020,455 2/1962 Reifel..317/250 3,283,226 11/1966 Umpleby et al ..317/249 R 2,542,611 2 1951Zuck ..317/250 x 3,192,456 6/1965 Reifel e161. ..317/250 3,166,6961/1965 Furman ..317/250 3,413,497 11/1968 Atalla ..200/181 x FOREIGNPATENTS 0R APPLICATlONS 321,151 10/1929 Great Britain ..333 71 865,0934/1961 01661131161111 ..333/71 Primary Examiner-Herman Karl SaalbachAssistant Examiner-Saxfield Chatmon, Jr. Att0mey-C. Cornell Remsen, Jr.,Walter J. Baum, Percy P. Lantzy, .1. Warren Whitesel, Delbert P. Warnerand James B. Raden ABSTRACT An electromechanical resonator is providedincorporating a vibrating reed driven by electrostatic forces betweenitself and an output electrode. The output is represented by capacitancechanges between the reed and an output electrode. Multiple resonatorsmay be used to form band-pass filters and the like.

24 Claims, 25 Drawing Figures Patented Aug. 22, 1972 3,6855%3 8Sheets-Sheet l Attorney Pate med Aug.22,1972 3,66,53

a Sheets-Sheet 2 Patented Aug. 22, 1972;

8 Sheets-Sheet 5 Patented Aug. 22, 1972. 3,686,53

8 Sheets-Sheet 5 Patented Aug. 22, 1972 3,686,53

8 Sheets-Sheet 7 L M P1 4205 ug; (B)

Patented Aug. 22, 1972 8 Sheets-Sheet 8 E l EN Q8 EQQJ l. 3% bqm mfi-$CW E5 EEE 8 ELECTROMECHANICAL RESONATOR The invention relates toelectromechanical resonators.

The invention provides an electromechanical resonator including at leastone vibrator element vibratable in bending oscillations by electrostaticforces between itself and first electrode means, the output of theresonator being represented by capacitance changes between a vibratorelement and second electrode means.

The foregoing and other features according to the invention will bebetter understood from the following description with reference to theaccompanying drawings, in which:

FIGS. 1A and 1B respectively illustrate one arrangement for theelectromechanical resonator according to the invention and theequivalent circuit for this resonator,

FIGS. 2A and 28 respectively illustrate an electrostatic transducerwhich forms part of the resonator according to FIG. 1A and theequivalent circuit for the transducer.

FIGS. 3A and 3B respectively illustrate a modified arrangement of theresonator according to FIG. 1A and the equivalent circuit of thismodified'arrangement,

FIGS. 4A and 4B respectively illustrate another arrangement for theelectromechanical resonator according to the invention and theequivalent circuit for this resonator,

FIGS. 5A and 53 respectively illustrate a modified arrangement of theresonator according to FIG. 4A and the equivalent circuit of thismodified arrangement,

FIG. 6 illustrates a further modified arrangement of the resonatoraccording to FIG. 4A,

FIGS. 7A and 7B respectively illustrate another arrangement for theelectromechanical resonator according to the invention and part of theequivalent circuit of this alternative arrangement,

FIGS. 8A and 83 respectively illustrate a modified arrangement of theresonator according to FIG. 7A and the equivalent circuit of thismodified arrangement.

FIGS. 9, l0 and 11 illustrate multi-element electromechanicalresonatorsaccording to the invention,

FIGS. 12A to 12C respectively illustrate a multi-element arrangement ofthe electromechanical resonator according to FIG. 7A and the equivalentcircuits of this arrangement, FIG. 13 illustrates a multi-elementelectromechanical resonator according to the invention with mechanicaland electrical coupling between the elements, I

FIGS. 14A and 14B respectively illustrate a further arrangement of theelectromechanical resonator ac cording to the invention and theequivalent circuit of this further arrangement, and

FIG. 15 illustrate a frequency response curve for a modified arrangementof the electromechanical resonator according to FIG. 12A,

In its simplest form the electromechanical resonator according to theinvention is a frequency dependent variable capacitance forming anelectromechanical transducer. Referring to FIG. 1A of the drawings, thedevices vibrator element 1 forms the mechanical part of the transduceras well as the moving plate of the variable capacitance. The vibratorelement spans over a conducting plate 2 which forms the second plate ofthe variablecapacitance. The vibrator element is of length l and isfixed at one end to a ground plane 3. The ground plane which isconnected to the input G1 via a capacitance C is biased above earthpotential by means of a d.c. voltage source B1, the positive side ofwhich is connected to the ground plane via a high impedance representedby the resistance R1. The resistance Rl and d.c. voltage source B1 areshunted by a decoupling-capacitance C The output of the resonator istaken across a load capacitance C connected between the plate 2and earthpotential and shunted by a resistance R3. The incoming signal to thevibrator element causes a variable electrostatic force to act on themetallic element and excites it into flexural vibra tion correspondingto its natural frequency. The vibrating element causes small variationsin the capacitance between itself and the plate 2 and this variation isdetected across the capacitance C to provide the resonator output. Thenatural frequency of the resonator is dependent on the material andphysical dimensions of the vibrator element as well as the boundaryconditions between the element and its surroundings.

The electrostatic force between two conducting surfaces depends on thesquare of the voltage between them. Hence, to avoid frequency doubling alarge d.c. bias voltage B1 is required as shown in FIG. 1A. This biasvoltage is also necessary for the operation of the output transducer andto provide the required sensitivity which increases linearly withincreases in bias voltage.

The equivalent circuit of the resonator according to FIG. 1A isillustrated in FIG. 1B of the drawings. Assuming that the movement ofthe vibrator element about an equilibrium position i.e. the positionwhen the electrostatic force is balanced by the restraining elasticforce in the material of the element, is small and that the voltagevariation about a mean biasing voltage E is also small then linearaction can be obtained.

Considering, the components of the equivalent circuit the equationsoutlined below give their relation ship with the electromechanicalresonator.

When there is a voltage E between the vibrator element 1 and the plate 2then this gives rise to an electrostatic force F given bylF|=VzE(de/d.x) (I) where C is the capacitance between the plate 2 andthe resonator element 1, x is the displacement of the vibrator element 1from itsequilibrium position and is equal to (1 -11,

d is the distance between the plate 2 and the vibrator element 1, and dis the value of d when E is zero.

E is the total voltage across the plate 2 and the vibrator element 1, Iand (dc/dx) is the rate of change of C with respect to x. At theequilibrium position the values of E, C and d are respectively E C and dE=[E +esin mt] where e is the peak value of the ac. driving voltage.

If E e and x is small, then the operation is practically linear and theelectrostatic force component due to the input signal is proportional toE e sin wt. Hence the sensitivity of the resonator is considerablyincreased.

For a rectangular vibrator element the capacitance The electrostatictransducer which forms part of the of the transducer C (a! We,,)/(d,,x)Farads 3 electromechanical resonator according to FIG. 1A and 2 itsequivalent circuit are respectively illustrated in zelwfo FIGS. 2A and28.

L. n .9... ,fi. The references used for the elements of the whereequivalent circuit according to FIG. 2B are the same as lis the lengthof the vibrator element and have the same relationships as thereferences used a is the ratio of the length of the plate 2 to thelength in the equivalent circuit according to FIG. 1A. This apof thevibrator element. plies also to the equivalent circuits which will be Wis the width of the vibrator element and s is the discussed insubsequent paragraphs.

dielectric constant for air and thus for small move- The equivalentcircuit according to FIG. 28 uses the ment the change in capacitancevaries linearly impedance analogy between electrical and mechanical withx when x is small in value. networks and it was arrived at by setting upLagranges The equivalent parameters of the vibrator element energyequations for generalized forces and co-orare L C and r dinates in themechanical and electrical parts of the L [equivalent to mass (M)]1.23plA Kgm (4) transducer according to FIG. 2A. These equations arewhere p is the density of the material of the vibrator as shown below:element, and A is the area of the vibrator element i.e. W

X t (thickness) d y) 5U a? (09:) a Compliance C [equivalent to Ystiffness (s) d (5y l 1 and Z Z 5 5 V (10) C 15 21, g metre] Newtonwhere o a .s. .1 t A, "w (5) f ande are generalized forces 7 x and q aregeneralized co-ordinates where Y Youngs modulus of elasticity. Lossesdue )is the kinetic energy of the system to mping em m o uQ) Where Q ise q U is the potential energy of the system ty factor of the resonantcircuits and (0 is the resonant f and x are respectively the force onand the displacequ n y 1/ u ument of the mechanical side of thetransducer If an ideal transformer i.e. the transformer T1 in FIG. 8 d qare res ctively the voltage and the charge on IE, with an impedanceratio is used between the th le tri l side, electrical and themechanical Parts of the transducer The kinetic energy of the transduceraccording to i then L C and r can be expressed in terms of Hen- FIG. 2Ais given by the expression ries farads and ohms respectively providedthat is x2 representing the value of the electromechanicaltransformation ratio of an electrostatic transducer. Thus Where M is themass of the moving element 1 and qo o 40 it is the velocity of themechanical side of the transwhere q is the charge across the element andthe plate (meet Y 2 at the equilibrium position and equals n o- Thepotential energy of the'transduce'r is the sum of the Theelectromechanical coupling coefficient m is elastic energy of themechanical parts, the electrostatic given y the ratio t/(Qa fl for arectangular energy of the electrical part, and the electrical energyelement and small displacements can be estimated due to the biasvoltage. However, if the equilibrium from the fellowihg equation:position is used as a reference some of the potential k 1g E 6 l 1energy terms will cancel out.

m T 15.2 Y td The ideal transformer ratio dz in FIG. 2B is equal to q ldThus it can be seen that for an ideal electro- Equation (7) shows that Kis dependent on the e static transducer using the impedance analogy, asis feetive length of the Plate 2, the a the the case with the equivalentcircuit of FIG. 2B, the material of the vibrator element and its lengthand f ll i relations are ti fi d:

thickness, and the gap between the vibrator element and the plate. The ef (qo/ o) 8 ([2) Due to the negative capacitance factors of the plates,V and the current i q= q.,/d it A g (13) the compliance of the vibratorelement is increased If two identical ideal transducers, as above, arecon slightly and the effective compliance is given by the folnectedtogether by their mechanical parts to form a sinlowing equation: gleunit and the electrical part of one of the transducers 1 C ff ti C 1 2 22 is made the input whilst the electrical part of the other I M e cc V6g j k2 a (8 of the transducers is made the output, then it can be andthe resonance frequenc then appears to be shifted Show on applymg theboundaIy commons that to l/(21r) w/l/(L C effective) from the naturalp2= (l/z) pl (14) resonance frequency of the element i.e. l/( 211') Theresistance R2 is the source resistance of the Where input G1 and theoutput of the resonator is taken p and p are the voltages associatedwith the electriacross the load resistance R3 and the capacitance calparts of the said one of and the said other of the Cow. transducersrespectively, and

r', and are the currents associated with the electrical parts of thesaid one of and the said other of the transducers respectively.

The above equations (14) and thus show an inversion between the inputand output of the single unit which can be allowed for by taking say theoutput transformer ratio (1) to be of opposite sign to the inputtransformer ratio (b It should be noted that the bias voltage B1 couldbe connected to the plate 2 instead of the vibrator element 1 if this isfound to be more convenient.

The electromechanical resonator can alsobe driven with the variablecapacitance C shunting the rest of the circuit as shown in FIG. 3B whichillustrates the equivalent circuit of the resonator illustrated in FIG.3A. In this arrangement, the plate 2 provides the input and the outputelectrode for the resonator. The input and the output are connected tothe plate2 respectively via appropriate capacitances C and C.

The electromechanical resonator according to the invention can have morethan one conducting plate, for example as illustrated in FIG. 4A whereintwo plates 4 and 5 are utilized. In this case it can be driven as a twoterminal or as a four terminal network. The equivalent circuit of a twoplate four terminal resonator is illustrated in FIG. 4B wherein it canbe seen that an additional transformation is introduced i.e. thetransformer T2 and the variable capacitance C2 of the second plate isalso included.

The bias voltage can be applied separately to the two plates 4 and 5 asillustrated in FIG. 5A. The equivalent circuit of this arrangement as atwo plate four'terminal resonator is illustrated in FIG. 5B wherein itcan be seen that an additional transformation is introduced i.e. thetransformer T2 and the variable capacitance C2 of the second plate isalso included.

The plates 4'and 5 can be on opposite sides of the vibrator element asillustrated in FIG. 6.

The bias voltages on the plates can have the same polarity when theplates 4 and 5 are on the same side of the vibrator element. In thiscase the ratios 41), and of the transducers will have opposite signs,and the overall transformer ratio will be negative. The plates 4 and 5can as previously stated be on opposite sides of the vibrator elementand have the same polarity of bias; in this case the ratios d), and willhave the same sign. They can also be on the same side of the vibratorelement but with different polarities of bias, and in this case and (1)will again have the same sign and the overall ratio positive. Theelectromechanical resonator could have more than two plates and theoverall transformer ratio between any two plates can be chosen to bepositive or negative depending on the relative position of the platesand the polarities of the bias voltages.

By having electrostatic input and output transducers, the resonator hasa direct capacitive coupling i.e. the capacitance C12 in FIGS. 4B and5B, between the input and output plates. This direct coupling willintroduce an attenuation peak higher or lower than the resonancefrequency depending on whether the overall transformer ratio is positiveor negative respectively. Controlling the value of the direct couplingwill allow variation in the position of the attenuation peak and thefrequency selectivity of the resonator. The direct coupling shouldhowever be kept as small as possible to improve the selectivity of theresonator. The input and I output plates can be isolated from each otherby using a tromechanical resonator according to the invention can beextended to an N-port network to cover an N- plate device. For example,in FIGS. 8A and SE a resonator having five plates is illustrated. Inthis arrangement the plates 9 and 11 are connected to earth potential,the plate 12 and the element 1 form the input transducer and the plates8 and 10 and the element 1 form the output transducers. Earthing a platewill effectively cause a slight shift in the resonance frequency due tothe negative capacitance of the corresponding port. It will alsoslightly increase the effective capacitance C, of the element 1 to earthby the addition of the corresponding capacitance of the earthed plate tothe element 1.

FIG. 88 illustrates the equivalent circuit of the five plate resonatoraccording to FIG. 8A where 2F is the total force in the system and k isthe system loop velocity. With a closed loop 2F will be equal to zero.

If a plate is situated on the opposite side of the vibrator element tothe plate 12, or if an extra bias voltage is used on a plate then the(1) associated therewith should take the appropriate sign.

By using multiplate resonators, higher order networks can be obtained.The five plate resonator according to FIG. 8A could be modified suchthat it functions as a band pass filter with two attenuation peaks i.e.one in the upper stop band and one in the lower stop band by having theplates 9 and 11 connected to earth potential, the plate 10 and theelement 1 forming the input transducer, the plates 8 and 12 and theelement 1 fonning the output transducers and the plate 8 biased positivewith respect to the element 1 potential. Alternatively, in order toobtain the same result an output transducer can be formed by the plate10 and the element 1, input transducers can be formed by the plates 8and 12 and the element 1, and in this instance the plates 9 and 11 wouldbe connected to earth potential and the plate 8 would be biased positivewith respect to the element 1 potential.

The electromechanical resonator can be made with more than one resonatorelement tuned to different frequencies, for example as illustrated inFIG. 9 and thereby provide a device which can be used in coding anddecoding equipment or selective calling systems. Referring to FIG. 9 thevibrator elements 14 to 17 are of different lengths thereby giving riseto the different frequencies and are fixed at one end to a ground plane18. The application of the input signal and the dc. bias voltage to theresonator is effected in a manner as previously outlined and the devicecan be operated as before with a single plate 19 or with an additionalplate 20 which is illustrated by a chain dotted line.

The electromechanical resonator according to the invention can also havea multi-element system, with strips or rods supported at one or bothends or at the nodal points, with mechanical or electrical coupling,

between the elements, with electrical couplings between the plates, orboth thereby providing a more complex multi-element filter examples ofwhich are illustrated in FIGS. 10, ll, 12 and 13. i

The electromechanical resonator according to FIG. is provided withvibrator elements 21 to which are of the same length and fixed at oneend to a ground plane 28. An input plate 26 is provided which forms theinput transducer with the element 21 and an output transducer with theelement 25.

The vibrator elements are coupled to each other by means of a couplingelement 31 which is in the form of a strip, rod or the like. Thecoupling element 31 traverses each of the vibrator elements and issecured to each of them. The vibrator element 21 is also coupled to thevibrator element 24 by means of a coupling element 32 which is in theform of a strip, rod, or the like.

Vibrational energy generated at the vibrator element 21 by the inputtransducer is transmitted to the vibrator element 22 via the section ofthe coupling element 31 situated therebetween and to the vibratorelement 24 via the coupling element 32 which causes these vibratorelements to vibrate in a mode of mechanical vibrations. The vibrationalenergy generated at the vibrator element 22 is then transmitted to thevibrator element 23 via the section of the coupling element 31 situatedtherebetween which cause the element 23 to vibrate in a mode ofmechanical vibration. This process is repeated until the vibrationalenergy of each of the vibrator elements has been transmitted to the nextadjacent vibrator element via the respective section of the couplingelement 31. The mode of mechanical vibrations of the vibrator element 25is detected by the output transducer which provides an output signalthat has been filtered as desired. The coupling between non-adjacentvibrator elements produces attenuation peaks in the resonator outputsignal.

The electromechanical resonator according to FIG. 11 operates in exactlythe same manner as but is constructed differently to the resonatoraccording to FIG. 10. The only difference is that the vibrator elements22 and 24 are connected at one end to a ground plane instead of to theground plane 28.

In order to increase the frequency of operation, the vibrator elements21 to 25 could be connected at both ends between two ground planes andmechanically or electrically coupled to each other. This arrangementreduces the dimensional tolerances of the resonator and couplingelements and therefore makes them more economical to produce.

Referring to FIG. 12A, the electromechanical resonator illustratedtherein comprises two vibrator elements 29 and 32 which are respectivelyconnected at one end to ground planes 33 and 34. The vibrator elementsspan over a conducting coupling plate 35 and a T-shaped conducting plate36 which is connected to earth potential. The vibrator elements 29 and32 also respectively span over conducting plates 37 and 38 which eachform one plate of an electrostatic transplanes are each biased aboveearth potential by means of the dc. voltage sources B1, the positiveside of which is connected to the ground plane via a high impedancerepresented by the resistance R1. The plate 36 is the screen plate andisolates the plates 35, 37 and 38 from each other.

In operation, the vibrational energy generated at the element 29 by theinput transducer gives rise to a variable electrostatic force on theplate 35 which acts on the element 32 and causes it to vibrate in a modeof mechanical vibrations. These vibrations are detected by the outputtransducer which provides an output signal that has been filtered asdesired.

It can therefore be seen that the coupling between the elements 29 and32 is effected electrically.

The equivalent circuit of the resonator according to FIG. 12A isillustrated in FIG. 12B. The capacitance between the two elements isrepresented by the capacitance C15. The resistance R is normally zero ifonly one coupling plate is used. However, if the plate 35 is dividedinto two parts each part being associated with a separate one of theelements and the two parts are connected together via an amplifier unitthen the resistance R can be replaced by an amplifier in the equivalentcircuit.

FIG. 15 illustrates the frequency response of the electromechanicalresonator according to FIG. 12A when modified by biasing the plate 37above earth potential by means of a dc. voltage source, the positiveside of which is connected to the plate 37 via a high impedanceresistance, dividing the plate 35 into two parts, in a manner asoutlined in the preceding paragraph, and connecting the two partstogether by an amplifier unit. The value of the dc. voltage source usedto bias the plate 37 is greater than the value of the source Bl therebyallowing a positive overall transformer ratio to be obtained for thatpart of the resonator associated with the vibrator element 29 and anattenuation peak higher than the resonance frequency of the element 29.

The vibrator element 32 in this arrangement therefore has only one biasvoltage applied thereto and a negative overall transformer ratio willresult thereby giving rise to an attenuation peak lower than theresonance frequency of the element 32.

By connecting the two vibrator elements 29 and 32 in cascade in a manneras previously outlined gives rise to the frequency response illustratedin FIG. 15 which simulates the response of a band pass filter withattenuation peaks higher and lower than the mid-band frequency.

The resonance frequency fi, and the attenuation peak frequency f of eachhalf of the resonator when tested individually were as follows:

Half including Half including vibrator element 29 vibrator element 32f,, 4012 KHZ f, 3.980 KHz f.= 4.090 KH; 3,815 m (Bandwithk 36 KHz(bandwidtm 4 l KHz The vibrator elements 29 and 32 which were ofberyllium copper, had nominal dimensions of:

Length 2.0 mm Width W 0.2 mm Thickness r 0.025 mm As can be seen fromFIG. 15, the response of the cascaded elements had a 3 db bandwidth of.55 Hz. Wider bandwidths can however be obtained by shifting theresonance frequencies of the two vibrator elements provided that theresulting increased attenuation ripple in the pass band is acceptable.

The capacitances C12, C34 and C14 are respectively representative of thedirect coupling capacitance between the plates 37 and 35, the plates 35and 38 and the plates 37 and 38. These capacitances can in practice bemade very small by suitable arrangement of the layout of the elementsand the plates.

The capacitances C1, C2, C3 and C4 are respectively representative ofthe capacitance between the element 29 and the plate 27, the element 29and the plate 35, the element 37, and the plate 35 and the element 32and the plate 38.

The transformers associated with the input transducer and the transducerformed by the plate 35 and the element 29 have been combined to give asingle transformer with the ratio 1 Similarly, the transformersassociated with the output transducer and the transducer formed by theplate 35 and the element 32 have been combined to give a singletransformer with the ratio 1 v If the elements 29 and 32 are at the samepotential and R'is zero then the equivalent circuit of FIG. 128 can bereduced to give the equivalent circuit illustrated in FIG. 12C. Thecapacitance C represents the coupling between the vibrator elements; ifthe coupling is mechanical C represents the compliance of the couplingelement.

It will be appreciated that various other configurations of theelectrical and mechanical coupling arrangements outlined in precedingparagraphs are possible for the electromechanical resonators accordingto the invention.

Electrical and mechanical coupling are utilized in the electromechanicalresonator according to FIG. 13. This resonator comprises two of theresonators according to FIG. 1 and a third resonator without the plate2. The vibrator element of the third resonator is mechanically coupledto the vibrator element of one of the other two resonators via thecoupling element 39 and is electrically coupled to the vibrator elementof the other of the two resonators via the conducting coupling plate 40.The plates 2 and the vibrator elements 1 form the input and outputtransducers for the device.

There is a wide choice in the shape and the material of the vibratorelements and in the arrangement of the conducting plates. The vibratorelements can be in the form of a disc or plate and the conducting platescan also be in the form of discs or concentric rings under or above thedisc vibrator elements. This therefore allows obtained and a bandwidthwider than can be obtained with quartz crystals. Capacitance ratios ofthe order of 40 have been obtained on experimental devices. It willtherefore be appreciated that this feature of the resonators accordingto the invention gives rise to a multitude of various networkarrangements in ladder or lattice form; one of the simplest isillustrated in FIGS. 14A and 143.

As shown in FIG. 14A, the resonator illustrated therein utilizes two ofthe resonators according to FIG. 1 with the plates 2 coupledtogether'via an amplifier unit A. It should however be noted that theamplifier unit A could be omitted and the plates 2 would in thisinstance be directly coupled or formed by a single plate.

The equivalent circuit of the resonator according to FIG. 14A isillustrated in FIG. 14B. The input and output resonators arerespectively represented by those parts of the circuit enclosed by thechain dotted lines 41 and 42. The coupling capacitance between theresonators is represented by the capacitance C12. If the elements arescreened from each other or are at the same voltage then the capacitanceC12 will be very small i.e. will tend towards zero and therefore thecircuit tends toward a ladder network.

The electromechanical resonator can be biased with an ac. voltageinstead of or superimposed on the dc. voltage and thus it would underthese conditions act as a modulator circuit which can be useful inmultiplex channel translating equipment.

The device also offers the interesting possibilities for makingmicrominiature oscillators and transformers.

The electromechanical coupling coefficient of an electrostatictransducer is inversely related to the gap between the fixed and movingplates of the transducer. To obtain high electromechanical coupling thegap would have to be very small. This tends to increase the resistanceof the still air in the gap, to the movement of the element, and thusreduces the overall quality factor Q of the resonant element. The airresistance can be reduced and the Q of the circuit increasedconsiderably by enclosing the element and conducting plate or plates inan evacuated enclosure or by using a conducting plate with a mesh ofmicro holes in it to reduce the dash pot effect of the still air.

The electromechanical resonators according to the invention arecompletely passive and the activity comes only in the detector circuit.The passive tuned unit with its electrostatic transducers is areversible device, by variation of the coupling it can be madesymmetrical or unsymmetrical. Thefrequency range of the resonator isfrom a few hundred Hz to a few hundred KI-Iz. The limiting factor ismainly the physical dimensions, particularly the length. However, themost suitable range is l to 30 KHz. At low frequencies, below I KHZ, theeffect of environmental vibrations, if proved to be a problem, can bereduced by using a balanced resonant element, or a free-free arrangementwhere the vibrator element is supported at its nodal points.

The electromechanical resonators outlined in the preceding paragraphsare compatible with use in hybrid integrated circuits either as aseparate unit or as an integral part of a more complex network. Thus,the techniques could well provide the sharply tuned integrated circuitso often required.

It is to be understood that the foregoing description of specificexamples of this invention is made by way of example only and is not tobe considered as a limitation on its scope.

I claim:

1. An electromechanical resonator comprising first electrode meansincluding an input fixed electrode and an input electrically conductivevibrator element, second electrode means including an output fixedelectrode and an output electrically conductive vibrator element, andbias means for establishing an electric field between the members ofeach of said first and second electrode means, the input vibratorelement being operatively coupled to the output vibrator element andcaused to vibrate at its natural frequency solely by electrostaticforces between itself and said input fixed electrode resulting frommodulation of said electric field by an input signal applied thereto.

2. An electromechanical resonator as claimed in claim 1 wherein saidinput vibrator element is coupled to said output vibrator element so asto form a single vibrator unit functioning as both the input and theoutput vibrator elements.

3. An electromechanical resonator as claimed in claim 1 wherein saidinput vibrator element is elongated and anchored at one end to a groundplane and vibratable in bending oscillation about said anchored end bysaid electrostatic forces, the output of the resonator being representedby capacitance changes between said input vibrator element and saidoutput vibrator element, the latter being of corresponding electricalshape with the former.

4. An electromechanical resonator as claimed in claim 1 wherein thesecond electrode means and a third electrode means are placed adjacentto, and spaced apart from the same side of the vibrator element.

5. An electromechanical resonator as claimed in claim 2 wherein theoutput conductive vibrator element. of said second means is coupled tosaid third electrode means so as to provide a single conductive member.

6. An electromechanical resonator as claimed in claim 4 wherein thesecond electrode means are provided by a first conductive member,wherein a third electrode means are provided by a second conductivemember which is connected to an output terminal, wherein the first andsecond conductive members coupled together, wherein the vibrator elementis biased above earth potential and wherein the vibrator element isconnected to an input terminal.

7. An electromechanical resonator as claimed in claim 1 wherein thesecond electrode means and a third electrode means are adjacent to, andspaced apart from opposite sides of the vibrator element.

'8. An electromechanical resonator as claimed in claim 23 wherein thesecond electrode means includes at least one input conductive member,and wherein a third means includes at least one output conductivemember.

9. An electromechanical resonator as claimed in claim 1, wherein theresonator includes a single vibrator element, and the resonators inputand output terminals are each connected to the single conductive member.

10. An electromechanical resonantor as claimed in claim 1 wherein theresonators input terminal is connected to the vibrator element.

11. An electromechanical resonator as claimed in claim 1, wherein theresonator includes a plurality of vibrator elements which are eachadapted to vibrate in bending oscillators at a different frequency tothe other claim 5, which also includes, between adjacent conductivemembers,an additional conductive member which is connected to earthpotential, and which is adjacent to, and spaced apart from, the vibratorelement.

13. An electromechanical resonator as claimed in claim 1 which includesan electrical voltage source connected between the vibrator element andearth potential.

13. An electromechanical resonator as claimed in claim 1 which includesan electrical voltage source that is connected between earth potentialand each conductive member, and wherein the vibrator element isconnected to earth potential.

v15. An electromechanical resonator as claimed in claim 13 wherein theelectrical voltage source is a dc voltage source, the positive side ofwhich is connected, via a high impedance to the vibrator element, andthe negative side of which is connected to earth potential, and whereinthe high impedance and dc. voltage source are shunted by a decouplingcapacitance.

16. An electromechanical resonator as claimed in claim 8 wherein aplurality of output conductive members are provided which are eachconnected to a separate output terminal.

17. An electromechanical resonator as claimed in claim 8 wherein aplurality of vibrator elements are provided, wherein an input conductivemember is associated with one of the vibrator elements, wherein anoutput conductive member is associated with another one of the vibratorelements, and wherein the resonator includes coupling means situatedbetween adjacent vibrator elements.

18. An electromechanical resonator as claimed in claim 17 which alsoincludes coupling means situated between non-adjacent vibrator elements.

19. An electromechanical resonator as claimed in claim 17 wherein thecoupling means are either electrical.

20. An electromechanical resonator as claimed in claim 19 wherein theelectrical coupling means includes a conductive plate which is spacedapart from the vibrator elements, and which is arranged transverse tothe longitudinal axes of the vibrator elements.

21. An electromechanical resonator as claimed in claim 19 wherein theelectrical couplingmeans includes for each vibrator element, aconductive plate which is adjacent to, and spaced apart from theassociated vibrator element, and wherein each conductive plate isconnected to a separate one of the other conductive plates via anamplifier unit.

22. An electromechanical resonator as claimed in claim 6 wherein thefirst and second conductive members are coupled together via anamplifier unit.

23. An electromechanical resonator as claimed in claim 1 wherein theconductive members are each provided with a mesh of micro-holes thereinwhich are arranged to reduce air resistance between the member and theassociated vibrator element.

24. An electromechanical resonator as claimed in claim 1 which includesan evacuated chamber within which the electrode means are located.

1. An electromechanical resonator comprising first electrode meansincluding an input fixed electrode and an input electrically conductivevibrator element, second electrode means including an output fixedelectrode and an output electrically conductive vibrator element, andbias means for establishing an electric field between the members ofeach of said first and second electrode means, the input vibratorelement being operatively coupled to the output vibrator element andcaused to vibrate at its natural frequency solely by electrostaticforces between itself and said input fixed electrode resulting frommodulation of said electric field by an input signal applied thereto. 2.An electromechanical resonator as claimed in claim 1 wherein said inputvibrator element is coupled to said output vibrator element so as toform a single vibrator unit functioning as both the input and the outputvibrator elements.
 3. An electromechanical resonator as claimed in claim1 wherein said input vibrator element is elongated and anchored at oneend to a ground plane and vibratable in bending oscillation about saidanchored end by said electrostatic forces, the output of the resonatorbeing represented by capacitance changes between said input vibratorelEment and said output vibrator element, the latter being ofcorresponding electrical shape with the former.
 4. An electromechanicalresonator as claimed in claim 1 wherein the second electrode means and athird electrode means are placed adjacent to, and spaced apart from thesame side of the vibrator element.
 5. An electromechanical resonator asclaimed in claim 2 wherein the output conductive vibrator element ofsaid second means is coupled to said third electrode means so as toprovide a single conductive member.
 6. An electromechanical resonator asclaimed in claim 4 wherein the second electrode means are provided by afirst conductive member, wherein a third electrode means are provided bya second conductive member which is connected to an output terminal,wherein the first and second conductive members coupled together,wherein the vibrator element is biased above earth potential and whereinthe vibrator element is connected to an input terminal.
 7. Anelectromechanical resonator as claimed in claim 1 wherein the secondelectrode means and a third electrode means are adjacent to, and spacedapart from opposite sides of the vibrator element.
 8. Anelectromechanical resonator as claimed in claim 1 wherein the secondelectrode means includes at least one input conductive member, andwherein a third electrode means includes at least one output conductivemember.
 9. An electromechanical resonator as claimed in claim 1 whereinthe resonator includes a single vibrator element, and the resonator''sinput and output terminals are each connected to the single conductivemember.
 10. An electromechanical resonantor as claimed in claim 1wherein the resonator''s input terminal is connected to the vibratorelement.
 11. An electromechanical resonator as claimed in claim 1,wherein the resonator includes a plurality of vibrator elements whichare each adapted to vibrate in bending oscillators at a differentfrequency to the other vibrator elements.
 12. An electromechanicalresonator as claimed in claim 5, which also includes, between adjacentconductive members, an additional conductive member which is connectedto earth potential, and which is adjacent to, and spaced apart from, thevibrator element.
 13. An electromechanical resonator as claimed in claim1 which includes an electrical voltage source connected between thevibrator element and earth potential.
 14. An electromechanical resonatoras claimed in claim 1 which includes an electrical voltage source thatis connected between earth potential and each conductive member, andwherein the vibrator element is connected to earth potential.
 15. Anelectromechanical resonator as claimed in claim 13 wherein theelectrical voltage source is a DC voltage source, the positive side ofwhich is connected, via a high impedance to the vibrator element, andthe negative side of which is connected to earth potential, and whereinthe high impedance and DC voltage source are shunted by a decouplingcapacitance.
 16. An electromechanical resonator as claimed in claim 8wherein a plurality of output conductive members are provided which areeach connected to a separate output terminal.
 17. An electromechanicalresonator as claimed in claim 8 wherein a plurality of vibrator elementsare provided, wherein an input conductive member is associated with oneof the vibrator elements, wherein an output conductive member isassociated with another one of the vibrator elements, and wherein theresonator includes coupling means situated between adjacent vibratorelements.
 18. An electromechanical resonator as claimed in claim 17which also includes coupling means situated between non-adjacentvibrator elements.
 19. An electromechanical resonator as claimed inclaim 17 wherein the coupling means are either electrical.
 20. Anelectromechanical resonator as claimed in claim 19 wherein theelectrical coupling means includes a conductive plate which is spacedapart from the vibrator elements, and which is arranged transverse tothe longitudinal axes of the vibrator elements.
 21. An electromechanicalresonator as claimed in claim 19 wherein the electrical coupling meansincludes for each vibrator element, a conductive plate which is adjacentto, and spaced apart from the associated vibrator element, and whereineach conductive plate is connected to a separate one of the otherconductive plates via an amplifier unit.
 22. An electromechanicalresonator as claimed in claim 6 wherein the first and second conductivemembers are coupled together via an amplifier unit.
 23. Anelectromechanical resonator as claimed in claim 1 wherein the conductivemembers are each provided with a mesh of micro-holes therein which arearranged to reduce air resistance between the member and the associatedvibrator element.
 24. An electromechanical resonator as claimed in claim1 which includes an evacuated chamber within which the electrode meansare located.